
/* @(#)e_atan2.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 *
 */

/* atan2(y,x)
 * Method :
 *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
 *	2. Reduce x to positive by (if x and y are unexceptional):
 *		ARG (x+iy) = arctan(y/x)   	   ... if x > 0,
 *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
 *
 * Special cases:
 *
 *	ATAN2((anything), NaN ) is NaN;
 *	ATAN2(NAN , (anything) ) is NaN;
 *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
 *	ATAN2(+-0, -(anything but NaN)) is +-pi ;
 *	ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
 *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
 *	ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
 *	ATAN2(+-INF,+INF ) is +-pi/4 ;
 *	ATAN2(+-INF,-INF ) is +-3pi/4;
 *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
 *
 * Constants:
 * The hexadecimal values are the intended ones for the following
 * constants. The decimal values may be used, provided that the
 * compiler will convert from decimal to binary accurately enough
 * to produce the hexadecimal values shown.
 */

#include "fdlibm.h"

#ifdef _NEED_FLOAT64

static const __float64
    tiny = _F_64(1.0e-300), zero = _F_64(0.0),
    pi_o_4 = _F_64(7.8539816339744827900E-01), /* 0x3FE921FB, 0x54442D18 */
    pi_o_2 = _F_64(1.5707963267948965580E+00), /* 0x3FF921FB, 0x54442D18 */
    pi = _F_64(3.1415926535897931160E+00), /* 0x400921FB, 0x54442D18 */
    pi_lo = _F_64(1.2246467991473531772E-16); /* 0x3CA1A626, 0x33145C07 */

__float64
atan264(__float64 y, __float64 x)
{
    __float64 z;
    __int32_t k, m, hx, hy, ix, iy;
    __uint32_t lx, ly;

    EXTRACT_WORDS(hx, lx, x);
    ix = hx & 0x7fffffff;
    EXTRACT_WORDS(hy, ly, y);
    iy = hy & 0x7fffffff;
    if (((ix | ((lx | -lx) >> 31)) > 0x7ff00000) ||
        ((iy | ((ly | -ly) >> 31)) > 0x7ff00000)) /* x or y is NaN */
        return x + y;
    if ((((__uint32_t) hx - 0x3ff00000) | lx) == 0)
        return atan64(y); /* x=1.0 */
    m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */

    /* when y = 0 */
    if ((iy | ly) == 0) {
        switch (m) {
        case 0:
        case 1:
            return y; /* atan(+-0,+anything)=+-0 */
        case 2:
            return pi + tiny; /* atan(+0,-anything) = pi */
        case 3:
            return -pi - tiny; /* atan(-0,-anything) =-pi */
        }
    }
    /* when x = 0 */
    if ((ix | lx) == 0)
        return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;

    /* when x is INF */
    if (ix == 0x7ff00000) {
        if (iy == 0x7ff00000) {
            switch (m) {
            case 0:
                return pi_o_4 + tiny; /* atan(+INF,+INF) */
            case 1:
                return -pi_o_4 - tiny; /* atan(-INF,+INF) */
            case 2:
                return _F_64(3.0) * pi_o_4 + tiny; /*atan(+INF,-INF)*/
            case 3:
                return _F_64(-3.0) * pi_o_4 - tiny; /*atan(-INF,-INF)*/
            }
        } else {
            switch (m) {
            case 0:
                return zero; /* atan(+...,+INF) */
            case 1:
                return -zero; /* atan(-...,+INF) */
            case 2:
                return pi + tiny; /* atan(+...,-INF) */
            case 3:
                return -pi - tiny; /* atan(-...,-INF) */
            }
        }
    }
    /* when y is INF */
    if (iy == 0x7ff00000)
        return (hy < 0) ? -pi_o_2 - tiny : pi_o_2 + tiny;

    /* compute y/x */
    k = (iy - ix) >> 20;
    if (k > 60)
        z = pi_o_2 + _F_64(0.5) * pi_lo; /* |y/x| >  2**60 */
    else if (hx < 0 && k < -60)
        z = _F_64(0.0); /* |y|/x < -2**60 */
    else
        z = atan64(check_uflow(fabs64(y / x))); /* safe to do y/x */
    switch (m) {
    case 0:
        return z; /* atan(+,+) */
    case 1: {
        __uint32_t zh;
        GET_HIGH_WORD(zh, z);
        SET_HIGH_WORD(z, zh ^ 0x80000000);
    }
        return z; /* atan(-,+) */
    case 2:
        return pi - (z - pi_lo); /* atan(+,-) */
    default: /* case 3 */
        return (z - pi_lo) - pi; /* atan(-,-) */
    }
}

_MATH_ALIAS_d_dd(atan2)

#endif /* _NEED_FLOAT64 */
